X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Feja%2FTODO;h=fb89e5edc905cea8475fb2349b3318e4aad22947;hb=9dc3876d4313b1292111aa6ff56be168606fe9fd;hp=25ef99df92da5f41595c609cdea9ae5d245cd1fe;hpb=715376429ac1807f9dae782268fbf66275a09cc0;p=sage.d.git

diff --git a/mjo/eja/TODO b/mjo/eja/TODO
index 25ef99d..fb89e5e 100644
--- a/mjo/eja/TODO
+++ b/mjo/eja/TODO
@@ -1,23 +1,12 @@
-1. Finish DirectSumEJA: add to_matrix(), random_instance(),
-   one()... methods. Make it subclass RationalBasisEuclideanJordanAlgebra.
-   This is not a general direct sum / cartesian product implementation,
-   it's used only with the other rationalbasis algebras (to make non-
-   simple EJAs out of the simple ones).
+1. Add references and start citing them.
 
-2. Add references and start citing them.
+2. Profile (and fix?) any remaining slow operations.
 
-3. Implement the octonion simple EJA.
+3. When we take a Cartesian product involving a trivial algebra, we
+   could easily cache the identity and charpoly coefficients using
+   the nontrivial factor. On the other hand, it's nice that we can
+   test out some alternate code paths...
 
-4. Pre-cache charpoly for some small algebras?
-
-RealSymmetricEJA(4):
-
-sage: F = J.base_ring()
-sage: a0 = (1/4)*X[4]**2*X[6]**2 - (1/2)*X[2]*X[5]*X[6]**2 - (1/2)*X[3]*X[4]*X[6]*X[7] + (F(2).sqrt()/2)*X[1]*X[5]*X[6]*X[7] + (1/4)*X[3]**2*X[7]**2 - (1/2)*X[0]*X[5]*X[7]**2 + (F(2).sqrt()/2)*X[2]*X[3]*X[6]*X[8] - (1/2)*X[1]*X[4]*X[6*X[8] - (1/2)*X[1]*X[3]*X[7]*X[8] + (F(2).sqrt()/2)*X[0]*X[4]*X[7]*X[8] + (1/4)*X[1]**2*X[8]**2 - (1/2)*X[0]*X[2]*X[8]**2 - (1/2)*X[2]*X[3]**2*X[9] + (F(2).sqrt()/2)*X[1]*X[3]*X[4]*X[9] - (1/2)*X[0]*X[4]**2*X[9] - (1/2)*X[1]**2*X[5]*X[9] + X[0]*X[2]*X[5]*X[9]
-
-5. The main EJA element constructor is happy to convert between
-   e.g. HadamardEJA(3) and JordanSpinEJA(3).
-
-6. Profile the construction of "large" matrix algebras (like the
-   15-dimensional QuaternionHermitianAlgebra(3)) to find out why
-   they're so slow.
\ No newline at end of file
+4. Conjecture: if x = (x1,x2), then det(x) = det(x1)det(x2). This
+   should be used to fix the fact that det(x) is monstrously slow in
+   Cartesian product algebras, and thus randomly in the doctests.